Session 75: Advanced Partial Fractions

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Overview

Last session we learned to use partial fractions to integrate rational functions for which the degree of the numerator was less than the degree of the denominator, and where the denominator had particularly nice factors. In this session we learn how to use partial fractions under more adverse conditions.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Repeated Factors (00:12:00)

» Accompanying Notes (PDF)

From Lecture 29 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Quadratic Factors (00:13:00)

» Accompanying Notes (PDF)

From Lecture 29 of 18.01 Single Variable Calculus, Fall 2006

Worked Example

 

Integral of (x-11)/(x2+9)(x+2)

Lecture Video and Notes

Video Excerpts

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» Clip 1: Long Division (00:05:00)

» Accompanying Notes (PDF)

From Lecture 29 of 18.01 Single Variable Calculus, Fall 2006

Worked Example

 

Integral of x3/x2-1

Recitation Video

 

Partial Fractions Decomposition

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Lecture Video and Notes

Video Excerpts

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» Clip 1: Partial Fractions – Big Example (00:18:00)

» Accompanying Notes (PDF)

From Lecture 30 of 18.01 Single Variable Calculus, Fall 2006

 

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